The effects of a vertical magnetic field on Oscillatory Double-Diffusive Convection at low Prandtl number

Oscillatory double diffusive convection (ODDC) is a process that takes place in a fluid that is stably stratified with respect to composition, but unstably stratified with respect to temperature. It has been well studied in the hydrodynamic limit at low Prandtl number, as it plays a potentially important role in stars. There, it is known to give rise to the formation of stacked convective layers, separated by thin interfaces. Here we analyze it in the presence of a vertical magnetic field. We find that the presence of a magnetic field decreases the kinetic energy in the turbulence after the saturation of the primary instability, and that this decrease is more pronounced with stronger magnetic fields. The compositional flux is correspondingly decreased. We also find that the magnetic field postpones the onset of layer formation, and in some cases, stops it entirely. This can be explained using the gamma instability theory of Radko, 2003. We conclude by discussing our findings with applications to mixing in stars.